A car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solverA car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solver

According to the Pythagorean Theorem 1. b = 122. a = 1/4 for more detail scroll down.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as an equation: c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

1. To use the Pythagorean theorem to find the length of side b, you can use the equation: c^2 = a^2 + b^2. In this case, c = 15 and a = 9, so you can substitute those values into the equation and solve for b:

15^2 = 9^2 + b^2

225 = 81 + b^2

b^2 = 225 - 81

b^2 = 144

b = sqrt(144)

b = 12

2. In the second case a is unknown and the other two sides are in fraction form, so we can use Pythagorean theorem to find the value of a.

The equation is c^2 = a^2 + b^2

(5/12)^2 = a^2 + (4/12)^2

25/144 = a^2 + 16/144

a^2 = 9/144

a = sqrt(9/144)

a = sqrt(1/16)

a = 1/4

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The maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.

What are Lagrange multipliers?

Lagrange's multiplier is a mathematical technique used to find the maximum or minimum value of a function subject to certain constraints. It is named after Joseph-Louis Lagrange, who first introduced the method in the 18th century.

To use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y^2 - x^2 subject to the constraint 1/4x^2 + y^2 = 64, we need to first set up the Lagrange function:

L(x, y, λ) = y^2 - x^2 + λ(1/4x^2 + y^2 - 64)

We then find the partial derivatives of L with respect to x, y and λ:

∂L/∂x = -2x + λ(1/2x) = 0

∂L/∂y = 2y + λ(y) = 0

∂L/∂λ = 1/4x^2 + y^2 - 64 = 0

Solving these equations, we find the following solutions:

x = 0, y = 0, λ = -8

x = 8√2, y = 8√2, λ = 4

x = -8√2, y = -8√2, λ = 4

Now, we need to check these solutions to see if they satisfy the constraint 1/4x^2 + y^2 = 64. Only the first solution x = 0, y = 0 satisfies the constraint.

Hence, the maximum and minimum value of the function subject to the given constraint is f(0,0) = 0.

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an = an - 1 . 7; 4,802 is the recursive formula for the geometric sequence.

What exactly is a geometric series?

A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.

                             2, 4, 8, 16, 32, 64,..., which has a common ratio of 2, is an illustration of a geometric sequence.

2, 14, 98, 686, ...

as shown in total

2 * 7 = 14             14 * 7 = 98          98 * 7 =   686

So   aₙ = aₙ₋¹

     a₅   =   a₄  . 7

           =    686  . 7  =  4802

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The domain of the expression is all real numbers except where the expression is undefined.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money.

Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range. A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided.

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The length of the towel bar is 9.5 inches.

Length is used to measure distance, In the International System of Quantities, a quantity with the distance dimension is referred to as length. The majority of measurement systems select a base unit for length from which all other units are derived. The metre serves as the International System of Units' fundamental unit of length.

Suppose, the length of the towel bar is x inches

The distance from each end of the towel bar to the end of the door is 9

inches. So, the total width of the door will be:[(x+(9*2)]=(x+18) inches

Given that, the width of the door is 27 inches 27.5 So, the equation will be.

x+18=27.5

x=27.5-18=9.5

Thus, the length of the towel bar will be 9.5 inches.

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The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.

The integral that represents the volume of the tetrahedron is given by:

$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$$

Evaluating the integral, we get:

$$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx = \int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx = \int_0^1 \frac{1}{2} (1-x)^2\,dx = \frac{1}{6}$$

Therefore, the volume of the tetrahedron is $\frac{1}{6}$.

We first set up the integral that represents the volume of the tetrahedron. The integral is a triple integral, so it can be written as $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$. This integral is the volume of a 3-dimensional region enclosed by the limits $x \in [0,1]$, $y \in [0,1-x]$, and $z \in [0,1-x-y]$. This region is exactly the same as the volume of the tetrahedron because it is the same 3-dimensional region.

Next, we evaluate the integral. First, we integrate with respect to $z$, which gives us $\int_0^1 \int_0^{1-x} (1-x-y)\,dy\,dx$. Then, we integrate with respect to $y$, which gives us $\int_0^1 \frac{1}{2} (1-x)^2\,dx$. Finally, we integrate with respect to $x$, which gives us $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.

The volume of the tetrahedron with base being the triangle with vertices (0,0), (1,0) and (0,1) and fourth vertex lying above the point (0,0) at height 1 can be found by evaluating the triple integral $\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 1\,dz\,dy\,dx$, which evaluates to $\frac{1}{6}$. Therefore, the volume of the tetrahedron is $\frac{1}{6}$.

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The artist wants to paint a canvas that is proportional to the photograph, which measures 4 inches by 5 inches.

To calculate the proportionality, we will use the formula for converting inches to centimeters. 1 inch is equal to 2.54 centimeters. Therefore, 4 inches is equal to 10.16 centimeters and 5 inches is equal to 12.7 centimeters. Therefore, the artist should purchase canvases that are 10.16 centimeters by 12.7 centimeters in size. This will correspond to the following canvas prices: $6.43, $11.65, $18.47, and $22.80. By purchasing these canvases, the artist will ensure that the painting is proportional to the photograph.

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In the given case, the population is assumed to have a normal distribution.

When creating a confidence interval for the population mean with a sample size of 100, the population is taken to have a normal distribution. This is due to the Central Limit Theorem, which asserts that regardless of the population distribution's form, the distribution of the sample means approaches a normal distribution as the sample size increases.

Therefore, it is safe to infer that the population mean is normally distributed when the sample size is large enough, for instance, n>30. Additionally, it is also ideal to conclude that the population mean has a normal distribution since a sample size of 100 is greater than 30.

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Answer: [tex]a^{n}(n^{2}+n+1)[/tex]

Step-by-step explanation:

Since the equation a^n+a^n+1+a^n+2

= a^n+n*a^n+n^2*a^n

= a^n*(n^2+n+1)

Answer:

[tex] {a}^{n} ( {a}^{2} + a + 1)[/tex]

Step-by-step explanation:

Remember exponent product rule: [tex]a^{n+m}=a^n*a^m[/tex]

Rewritten: [tex]{a}^{n} + ( {a}^{n}* {a}^{1}) + ({a}^{n} * {a}^{2})[/tex]

factor the common factor [tex] {a}^{n} [/tex] to get

[tex] {a}^{n} (1 + a + {a}^{2} )[/tex]

reorder from highest exponent to get answer.

For the given Circumference, the radius of the circle is 364.50 feet, and diameter is 729 feet.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

A circle's circumference is equal to two times its radius or diameter, where r is the radius and d is the diameter. Where r is the circle's radius, the area of a circle is equal to πr2

The Circumference of the circle is 2289.1 sq. feet,

Circumference = 2πr

2289.1 = 2 π r

⇒ 2289.1 = 2 × 3.14 × r

⇒ r = 2289.1 / 6.28

⇒ r = 364.50

We know, Diameter = 2 × Radius

⇒ Diameter = 2 × 364.50 = 729

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Answer:

8 days

Step-by-step explanation:

We know

A project should take no more than 60 hours, which means the number of hours should [tex]\leq[/tex] 60 hours.

John can spare 7.5 hours per day to work on the project.

Let x represent the number of days; we have the equation

7.5x [tex]\leq[/tex] 60

x [tex]\leq[/tex] 8

So, the maximum number of days it will take him to finish is 8 days.

Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.

Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.

a. Olaf expects to get 1.8 broken eggs.

b. The standard deviation is 0.5.

c. Yes, it is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs, and if they are not independent, the probability of one carton containing broken eggs will influence the other cartons.

Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.

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The exponential depreciation rate to the nearest tenth of a percent is -0.2%. 

we need to use the exponential decay formula to find exponential rate.

A = A0 * e^(-rt)

where:

A0 = initial value of car (52,000)

A = final price of the car (45,000)

t = elapsed time (32 months)

r = exponential depreciation rate

Rearrange the formula to solve for the exponential depreciation rate "r".

r = -ln(A/A0) / t

Insert value:

r= -ln(45,000 / 52,000) / 32

r = -0.067115074/32

r = -0.002097288

The exponential depreciation rate, expressed as a percentage to the nearest tenth of a percent, is obtained by multiplying by 100.

r = -0.002097288 * 100

r = -0.21D

44 Therefore, the exponential depreciation rate to the nearest tenth of a percent is -0.2%. 

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The surface area S is given by the definite integral of the function :

|r(t) X r'(t)| over the interval [1], which can be approximated by numerical integration methods.

To find the surface area of the surface generated by the given equations, we need to first find the cross-sectional area of the surface at every point of t and then integrate it over the interval. To do this, we need to find the vector r(t) = (x(t),y(t)) and its derivative r'(t) = (x'(t),y'(t)) which gives the tangent vector to the curve at t. The cross-sectional area of the surface at t is given by the magnitude of the vector cross product of the vectors r(t) and r'(t) and is written as |r(t) X r'(t)|. Then the surface area S is given by the definite integral of this cross-sectional area over the interval [1].

The definite integral can be solved analytically or numerically, however, the final answer would be the integration of the function |r(t) X r'(t)| over the interval [1], which is not possible to solve analytically, so we use numerical integration methods.

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Answer:

-216

Step-by-step explanation:

[tex]-6^3\\-6*-6*-6 = -216[/tex]

V is a set of functions that map from [tex]R^5[/tex] to R. It is a vector space because it has a commutative addition operation, a zero vector, additive inverses, scalar multiplication that distributes over vector addition, associativity of vector addition, a multiplicative identity for scalars, and a multiplicative inverse for non-zero scalars.

cf(x) + cg(x) for all real numbers x.

Associativity of vector addition: Let f, g, and h be any vectors in V. Then (f + g) + h = f + (g + h) for all real numbers x.

Existence of a multiplicative identity for scalars: The multiplicative identity for scalars in V is 1, such that for any vector f in V, 1f(x) = f(x) for all real numbers x.

Existence of a multiplicative inverse for nonzero scalars: For any nonzero real number c, there exists a multiplicative inverse 1/c such that c(1/c)f(x) = f(x) for all real numbers x and for any vector f in V.

All these properties are the standard conditions for a vector space, therefore V is a vector space.

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Answer:

12

Step-by-step explanation:

There are 6 common factors of 12 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 60 is 12.

The distributive property is used eliminate the parentheses in the equation and the solution of the equation is not correct.

Part A: The distributive property can be used to eliminate the parentheses in the equation.

Part B: Using the distributive property, we get:

-10 + 6h - 48 = -8h - 12

6h + 8h = 48 + 10 -12

14h = 70

Now we divide both sides by 14:

h = 70/14

h = 5

Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.

-10 + 6(5 - 8) = -4(2(5) + 3)

-10 + 6(-3) = -4(10 + 3)

-10 - 18 = -4(13)

-28 = -52

Thus, the solution is not correct.

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Answer:

Part A: The distributive property can be used to eliminate the parentheses in the equation.

Part B: Using the distributive property, we get:

-10 + 6h - 48 = -8h - 12

6h + 8h = 48 + 10 -12

14h = 70

Now we divide both sides by 14:

h = 70/14

h = 5

Part C: To verify the solution, we can substitute 5 back into the original equation and see if both sides are equal.

-10 + 6(5 - 8) = -4(2(5) + 3)

-10 + 6(-3) = -4(10 + 3)

-10 - 18 = -4(13)

-28 = -52

Thus, the solution is not correct.

Step-by-step explanation:

Answer:

مرتم باشگاه ورزشی خیلی علاقه داشتم خیلی قشنگ بی که خیلی تخفیف فایل که خیلی خوعه بچه آخر بی

Answer:
After four bites, Alice would be 256 inches tall.

An exponential function that models this growth would be f (x) = 64.22 where x is the number of bites she takes.

If Alice doesn't take any bites (zero bites), her height would be 64 inches.

are true statements.

If Alice takes two bites, she will be 256 inches tall. is false and After three bites, Alice would be 192 inches tall is also false.

Answer:

2(2p+5)

Step-by-step explanation:

4p + 10

taking common values

2(2p+5)

The expression 4p + 10 can be factored by grouping the like terms together.

4p + 10 can be factored as:

2(2p + 5)

This is the prime factorization of the given expression. Here we have factored out the common factor 2 from 4p and 10. This is the most simplified form of the expression.

The numbers in table are in proportion. Therefore, option B is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Here,

From the table A:

1/5 = 3/15 = 5/20 = 7/28

1/5 = 1/5 ≠ 1/4 = 1/4

Here, numbers are not in proportion.

From the table B:

3/9 = 5/15 = 7/21 = 8/24

1/3 = 1/3 = 1/3 = 1/3

The numbers are in proportion.

From the table C:

4/12 = 6/18 = 7/28 = 9/36

1/3 = 1/3 ≠ 1/4 ≠ 1/4

The numbers are not in proportion.

From the table D:

2/8 = 3/12 = 4/16 = 5/30

1/4 = 1/4 = 1/4 ≠ 1/6

The numbers are not in proportion.

Therefore, option B is the correct answer.

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The medians of a triangle connect the midpoints of each side and intersect at the centroid of the triangle.

Medians of a triangle are lines that connect the midpoints of each side of the triangle to the opposite vertex. This means that they divide the triangle into two halves, each with an area that is equal to half of the area of the entire triangle. The medians of a triangle with vertices (a1, a2, a3) intersect at a point known as the centroid of the triangle, which is located at the intersection of the three medians. The centroid can be found by taking the average of the three vertices, or by finding the intersection of the three medians. The centroid is the point at which the three medians of the triangle intersect and is the center of gravity for the triangle. In other words, it is the point that all three medians will intersect at.

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The answers to all parts is shown below.

An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labelling. Thus, mathematics is built on numbers.

1. Real numbers are "closed" under addition Integers are "not closed" under division. Irrational numbers are "not closed" under multiplication. Rational numbers are "closed" under subtraction.

2. Rational numbers are "closed" under subtraction. If an operation is closed under a set of numbers that means that the result of the operation will always be within that same set of numbers.

3. The  closure property of multiplication holds for natural numbers, whole numbers, integers and rational numbers.

4. Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.

5. The whole number system and the polynomial system are nearly identical. Actually, there are not many differences between polynomial functions and our whole number system. We employ a base-10 (decimal) approach for counting. The above-mentioned polynomial is an example of a "base x" system.

6. The system of polynomials is almost the same with the system of whole numbers.

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Answer:

a.7a-ab+b

=7×3-3×5+5

=21-15+5

=11

b.10a÷(2b)

=10×3÷(2×5)

=30÷10

=3

C.4ab-6b+5a

=4×3×5-6×5+5×3

=60-30+15

=45

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The y-intercept of the given line is 100.

What is the y-intercept?

The y-intercept is the point at which the line crosses the y-axis, which occurs when x = 0. To find the y-intercept, we can plug in x = 0 into the equation of the line.

We can write the equation of the line in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

We can find the slope m using the point slope formula:

m = (y2 - y1) / (x2 - x1) = (148-100)/(42-0) = 48/42 = 4/3

Now we can substitute the point (0,100) into the equation of the line:

y = (4/3)x + b

100 = (4/3) * 0 + b

b = 100

So the y-intercept is (0,100)

Hence, the y-intercept of the given line is 100.

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The features of the given polynomial graph are;

A) Domain: (-∞, ∞)

Range: (-∞, 16)

B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)

C) The y-intercept is; (0, 0)

D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)

E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) Even function

The domain of a function is defined as the set of all possible input values for which the function holds. The range of a function is defined as the set of all possible output values for all possible input values.

A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.

B) The x-intercepts are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)

C) The y-intercepts are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)

D) Looking at the given graph, it is increasing when the curve rises  and in this case it is; (-∞, -2) and (0, 2)

E)  Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) The function is an even function

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Ages in order starting with the oldest : ken , natalie , melissa ,  jason.

Heights in order starting with the tallest : natalie, ken , jason , melissa.

by descending order.

From the information given in the question :

natalie (N) is older than melissa (M)

melissa (M) is older than jason (J)

ken (K) is older than natalie (N)

So , similarly ken is the oldest among those 4. and then order follows as natalie older than melissa older than jason.

                        K>N>M>J

jason (J) is taller than melissa (M)

natali (N) is taller than ken (K)

ken (K) is taller than jason (J)

So, similarly natali is the tallest among all 4, and then order follows as

ken taller than jason taller than melissa.

                        N>K>J>M

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Answer: 126

Step-by-step explanation: Given that the median is the middle number in a sorted, ascending, or descending list of numbers and can be more descriptive of that data set than the average. We know that we need to put the numbers in order from greatest to least or least to greatest first.

Step 1: Ordering the numbers (from least to greatest)

98,118,121,126,127,132,134

Step 2: Finding the value in the middle

98,118,121,  126  ,127,132,134

We now know that 126 is the median number of people served.

Answer: 126 is the median number of people served.

Step-by-step explanation:

The median is found by arranging the data points in a set from lowest to greatest. Once this is done, if there are an odd number of data points, simply find the number in the middle. If there is an even number, find the average of the two middle numbers. Here, you would arrange the numbers as such, 98,118,121,126,127,132,134. Once this is done, since there are seven lines (an odd number of data points, therefore), figure out which number is in the middle, and here it is 126. Hence, the median is 126 (people)

Shawn should use the point-slope formula ⇒ y - y₁ = m(x - x₁) and the y-intercept is -12.

We already know that the point-slope formula goes as such -

⇒ y - y₁ = m(x - x₁)

We have also been told that the slope of the line is 4 and the line passes through the point (1,-8). So, point (1,-8) = (x₁ , y₁) and the slope, m = 4.

Using the given values and the formula of point-slope, we get -

⇒ y - (-8) = 4(x - 1)

⇒ y + 8 = 4x - 4

⇒ 4x - y = -12

⇒ y = 4x - 12

This is the equation of the line.

From this, we get the y-intercept = -12

The complete question that you might be looking for is given below -

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept, and what is the y-intercept of the line?

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Answer:

Cross section at z = -1: y = 3(-1)^2 - 3x^2 = -3x^2

Cross section at z = 0: y = 3(0)^2 - 3x^2 = -3x^2

Cross section at z = 1: y = 3(1)^2 - 3x^2 = -3x^2

Cross section at y = -1: x^2 = (3z^2+1)/3; x = sqrt((3z^2+1)/3) or x = -sqrt((3z^2+1)/3)

Cross section at y = 0: x = 0;

Cross section at y = 1: x^2 = (3z^2-1)/3; x = sqrt((3z^2-1)/3) or x = -sqrt((3z^2-1)/3)

Cross section at x = -1: z^2 = (3y+1)/3; z = sqrt((3y+1)/3) or z = -sqrt((3y+1)/3)

Cross section at x = 0: z = 0;

Cross section at x = 1: z^2 = (3y-1)/3; z = sqrt((3y-1)/3) or z = -sqrt((3y-1)/3)

Step-by-step explanation: